A variety of technologies have been developed which assist the driver of a vehicle. For example, there is driving assistance for avoiding a collision between a host vehicle and an obstacle (another vehicle, a walker, and the like). In driving assistance for avoiding a collision, for example, there are emergency avoidance assistance (Pre Crash Safety (PCS) or the like) and prediction assistance. Emergency avoidance assistance is assistance for avoiding collision in the timing when the obstacle exists closely in front of the host vehicle, a collision is apparent from a current relative position and a relative speed of the host vehicle and the obstacle, and there is no time to spare before the collision. In addition, even when there is no possibility of collision at the present time, if any change of the host vehicle and the obstacle (for example, a walker walking on the roadside jumps out into the roadway) is considered, there is a case where the possibility of a future collision arises. Here, prediction assistance is assistance for avoiding a future collision (a collision that is farther in time and distance than imminent collision subject to emergency avoidance assistance) in advance by predicting the possibility of a future collision between the host vehicle and an obstacle in consideration of various future situations of the host vehicle and the obstacle when there is time to spare before the collision. In Patent Literature 1, a technology is disclosed in which a risk potential of an obstacle around a host vehicle is calculated and driving operation is assisted based on the risk potential.